Abstract

The primary aim of the work reported in this paper is to elucidate the relationship between discrete and continuous deterministic representations of spatial population processes. Our experimental vehicle is a spatially explicit version of the Rosenzweig-McArthur model with immobile prey and a diffusively dispersing predator. We find that careful formulation of the discrete representation leads to essentially complete behavioral concordance between the two representations. We examine the invasions that follow localized introduction of predators into such a system and show that the biological realism of the model predictions can be greatly enhanced by preventing in situ regrowth of predator populations from densities that should be interpreted as representing local extinction. We exploit the close concordance of behavior between continuous and discrete representations by using the discrete version to perform a wide range of numerical experiments on one-dimensional and two-dimensional systems, while turning to the continous version to provide approximate analytic results for the natural time and space scales of the predicted population patterns. We conclude by discussing the implications of our findings for the experimental and theoretical study of spatial population dynamics.